On the robustness to adversarial corruption and to heavy-tailed data of the Stahel–Donoho median of means

Articles

On the robustness to adversarial corruption and to heavy-tailed data of the Stahel–Donoho median of means

Année

2023

Auteurs

Abstract

We consider median of means (MOM) versions of the Stahel–Donoho outlyingness (SDO) [ 23, 66] and of the Median Absolute Deviation (MAD) [ 30] functions to construct subgaussian estimators of a mean vector under adversarial contamination and heavy-tailed data. We develop a single analysis of the MOM version of the SDO which covers all cases ranging from the Gaussian case to the L2 case. It is based on isomorphic and almost isometric properties of the MOM versions of SDO and MAD. This analysis also covers cases where the mean does not even exist but a location parameter does; in those cases we still recover the same subgaussian rates and the same price for adversarial contamination even though there is not even a first moment.

DEPERSIN, J. et LECUE, G. (2023). On the robustness to adversarial corruption and to heavy-tailed data of the Stahel–Donoho median of means. Information and Inference: A Journal of the IMA, 12(2), pp. 814-850.